INTEGRAIS

Question 1

. ∫1 dx

Answer 1

x+c

Question 2

. ∫x^r dx

Answer 2

1/(r+1)*x^(r+1)+c

Question 3

. ∫sin(ax) dx

Answer 3

-1/a*cos(ax)+c

Question 4

. ∫sec^2(ax) dx

Answer 4

1/a*tan(ax)+c

Question 5

. ∫sec(ax)*tan(ax) dx

Answer 5

1/a sec(ax) +c

Question 6

. ∫1/sqrt(a^2-x^2) dx

Answer 6

arcsin(x/a)+c

Question 7

. ∫-1/sqrt(a^2-x^2) dx

Answer 7

arccos(x/a)+c

Question 8

. ∫e^(a*x) dx

Answer 8

1/a* e^(a*x) + c

Question 9

. ∫cosh(ax) dx

Answer 9

1/a sinh(ax) + c

Question 10

. ∫ 1/x dx

Answer 10

ln|x| + c

Question 11

. ∫cos(ax) dx

Answer 11

1/a sin(ax) + c

Question 12

. ∫csc^2(ax) dx

Answer 12

-1/a cot(ax) + c

Question 13

. ∫csc(ax)*cot(ax) dx

Answer 13

-1/a csc(ax) + c

Question 14

. ∫ 1/ (a^2+x^2) dx

Answer 14

1/a arctan(x/a)+c

Question 15

. ∫b^(a*x) dx

Answer 15

1/ (a*ln|b|) b^(ax) + c

Question 16

. ∫tan(x) dx

Answer 16

ln|sec(x)|+c

Question 17

. ∫cot(x) dx;

Answer 17

ln|sin(x)| + c = - ln|csc(x)| + c

Question 18

. ∫sec(x)dx

Answer 18

ln|sec(x) + tan(x)| + c

Question 19

. ∫csc(x)dx

Answer 19

-ln|csc(x)+cot(x)| + c = ln|csc(x)-cot(x)| + c

Question 20

Teorema Fundamental do Cálculo

Answer 20

. ∫ f(x) dx = F(b) - F(a)

Question 21

Método de Substituição

Answer 21

u = g(x)
du = g’(x) dx
. ∫f’(g(x))*g’(x)dx = . ∫f’(u)du = f(g(x)) + c

Question 22

Integração por partes

Answer 22

. ∫ U * V’ = U * V * . ∫ V + U’